Non-isothermal Reactor Research Articles

Kinetics of the catalytic air oxidation of o-xylene over a commercial V 2O 5-TiO 2 catalyst

The gas-phase oxidation of o-xylene over a commercial V 2O 5-TiO 2 catalyst was studied in fixed bed non-isothermal reactor. The experiments were carried out at initial o-xylene concentrations which differed greatly from each other. The following reaction network was suggested. ▪ It is suggested to use the Langmuir-Hinshelwood kinetic model in which a surface reaction between o-xylene and oxygen, chemisorbed on separate active centres, is the limiting step. It seems that the redox model is not adequate for the kinetic description of o-xylene oxidation.

Transient Processing of Titanium Silicides in a Non-Isothermal Reactor

ABSTRACTTransient processing of titanium silicides on single-crystal Si in a non-isothermal reactor provides high quality films. Heat from quartz-hal?gen tungsten lamps and a small temperature gradient act as driving forces for the reaction. The temperature gradient, small compared to the concentration gradient, shows negligible influence on the formation process. The influence of sample reflectivity on the other hand is appreciable. From Xe+ marker experiments, Si atoms are found to be the moving species either up or down the temperature gradient. Small amount of TiSi as an intermediate phase is found to be coexistent with TiSi2. The silicide formation of the implanted wafers is somewhat slower than that of the unimplanted wafers.

The dynamic behaviour of continuous polymerization reactors—III: An experimental study of multiple steady states in solution polymerization

A study involving small scale reactor experiments coupled with detailed non-isothermal reactor modelling has been carried out shows that ‘isoia” ty

Experimental study of ignition and extinction waves and oscillatory behavior of a tubular nonadiabatic fixed bed reactor for the oxidation of carbon monoxide

An experimental study of axial temperature profiles in a nonadiabatic tubular fixed bed reactor has been made under the transient operation. The catalytic carbon monoxide oxidation occurring on a Pt/alumina catalyst has been used. Ignition and extinction waves have been studied both in a short and a long catalyst bed. It is shown that in a short bed ignition and extinction occur at the reactor outlet while for a long bed the ignition and extinction process takes place inside the reactor and is not influenced by the outlet part of the reactor. A systematic measurement indicates that in a narrow range of inlet parameters the integral nonadiabatic nonisothermal reactor may operate in an oscillatory state. These oscillations can be periodic or aperiodic.

Kinetic analysis of a non‐isothermal reactor: Comments on a note by Cooper and Alley

AIChE JournalVolume 29, Issue 1 p. 157-159 R&D Note Kinetic analysis of a non-isothermal reactor: Comments on a note by Cooper and Alley R. S. Upadhye, R. S. Upadhye Air Products and Chemicals, Inc., Allentown, PA 18105Search for more papers by this authorV. G. Fox, V. G. Fox Air Products and Chemicals, Inc., Allentown, PA 18105Search for more papers by this author R. S. Upadhye, R. S. Upadhye Air Products and Chemicals, Inc., Allentown, PA 18105Search for more papers by this authorV. G. Fox, V. G. Fox Air Products and Chemicals, Inc., Allentown, PA 18105Search for more papers by this author First published: January 1983 https://doi.org/10.1002/aic.690290123AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume29, Issue1January 1983Pages 157-159 RelatedInformation

The reaction engineering of electrochemical cells—I. Axial packed bed electrodes

It is shown that the graphical method of solving the coupled equations for an endothermic reaction in a plug-flow, non-isothermal reactor can be extended to electrochemical reactions in three-dimensional electrodes. The method of solution is described and as a first example, it has been applied to a simple reversible reaction in an axial packed bed electrode. The sensitivity to various parameters has been examined. The method is ideally suited to computer-aided design procedures.

The reaction engineering of electrochemical cells—II. Packed bed electrodes with orthogonal flow of current and solution

The analogy with an endothermic chemical reaction in a plug-flow non-isothermal reactor has been extended to the case of a packed bed electrode with orthogonal flow of current and solution (flow-by electrode). Comparison of the predicted (macrokinetic) polarisation curves with experimental ones obtained for equimolar ferri/ferrocyanide in alkaline solution in reticulated metal foam electrodes is satisfactory. Information on the microkinetics within the electrode is given implicitly. The sensitivity of the calculation to operating parameters is also discussed.

Kinetic analysis of a non‐isothermal reactor

AIChE JournalVolume 27, Issue 6 p. 1039-1041 Article Kinetic analysis of a non-isothermal reactor C. D. Cooper, C. D. Cooper Chemical Engineering Dept., Clemson University, Clemson, South Carolina 29631Search for more papers by this authorF. C. Alley, F. C. Alley Chemical Engineering Dept., Clemson University, Clemson, South Carolina 29631Search for more papers by this author C. D. Cooper, C. D. Cooper Chemical Engineering Dept., Clemson University, Clemson, South Carolina 29631Search for more papers by this authorF. C. Alley, F. C. Alley Chemical Engineering Dept., Clemson University, Clemson, South Carolina 29631Search for more papers by this author First published: November 1981 https://doi.org/10.1002/aic.690270627Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume27, Issue6November 1981Pages 1039-1041 RelatedInformation

An approximate approach to design and analysis of fixed‐bed catalytic reactors

AbstractAn approximate approach is proposed for the design and analysis of fixed‐bed catalytic reactors in which the intraphase diffusion is important. This approach makes it possible to transform the design and analysis problem of nonisothermal reactors with inter‐ and intraphase mass and heat transfer resistance into one of simply integrating a single equation with respect to concentration. This transformation is applicable to general from of kinetics. Exceptions are reaction rate forms that can exhibit empirical or approximate negative order behavior. The transformation is based on a generalized effectiveness factor or a reactor point effectiveness factor. While the design and analysis of two‐dimensional reactors requires simultaneous solution of conservation equations for mass and heat which are transformed into the equivalents of homogeneous reactors, the problem of one‐dimensional reactors with axial dispersion involves simple integration of a single mass conservation equation.

Design of a Chemical Pulse Reactor

Abstract The general reaction X + Y + M → P + M may - due to substrate inhibition at the catalytic site M - give rise to bistability phenomena in an isothermal tubular fixed bed reactor. The parametric conditions for bistability in the single pellet are studied by a numerical technique. Solution of the steady state equations for a two phase model of the tubular reactor shows that narrow zones with high conversion are possible, similar to ignition zones in nonisothermal catalytic reactors. By a cyclic operation with alternating periods of charging the catalyst phase with substrate and discharging it by chemical reaction, pulses of high product concentration can be generated at the reactor outlet. This is demonstrated by simulation of the system assuming low flow velocity as it is characteristic for reaction columns with liquid mobile phase.

The efficiencies of thermochemical energy transfer

A general thermodynamic study of thermochemical energy transfer and work production processes is presented. Both gaseous systems in which the effluent of each reactor is not separated into the reactant and product species, and liquid/gas systems in which the effluent separates spontaneously into liquid and gas phases, are treated. the study extends to consideration of non-isothermal reactors, to the individual roles of reactor and heat exchanger in the work production processes and to the significance of the intrinsic work of phase separation. the overall system efficiency is derived as the product of two efficiencies: the energy storage efficiency which defines the fraction of the input energy passed in chemical form to storage and the work recovery efficiency which defines the fraction of this stored energy available as output work. the fundamental thermodynamic processes underlying the derivation of these efficiencies are examined from the point of view of optimization of the design and operation of individual system components. In particular, it is shown that the available work from a thermochemical energy transfer system approaches the maximum value given by the Gibbs' free energy change when the temperature profile of the exothermic reactor is suitably tailored. The work of separation has formed the basis of the analysis of specific system components and has given a useful insight into the understanding of energy storage efficiency. Work recovery efficiencies are calculated for the ammonia/hydrogen-nitrogen system and the paper concludes with a discussion of some practical considerations relating to the recovery of work and the performance that one might ultimately expect from this system.

Nonisothermal reactors: Theory and application of thermal time distributions

For reactions in nonisothermal systems, the thermal time distribution is the analog of the residence time distribution. If the reaction can be characterized by a single activation energy, knowledge of the thermal time distribution based on this activation energy can be used to predict the yield of a first order reaction uniquely and to closely bound the yield for reactions of order other than first. Thermal time distributions are a useful conceptual and analytical tool for reaction engineering, particularly in systems where the temperature and velocity profiles are not strongly coupled to the extent of reaction. This situation frequently occurs in the processing of polymer melts, for example in the activation of blowing agents or in chemical modification of the polymer chain. Simplified flow models of heat exchange and extrusion equipment are used to illustrate the application of thermal time distributions and to show that they often differ significantly from the residence time distribution in the same device. In fixed wall heat exchangers, the thermal time distribution shows less uniform reaction conditions than would be true for an isothermal reaction governed by the residence time distribution. In extruders, and particularly for those where viscous dissipation is the major energy input, this situation is dramatically reversed with a reaction environment very similar to that for piston flow and substantially better than would occur in the same equipment operated isothermally.

Application of the Complex Method for Constrained Optimization to Oilfield Problems

Abstract In the application of optimization techniques, considerable difficulty is often encountered in determining the most applicable or effective method for solving a particular problem. In an attempt to solve this dilemma, M. J. Box developed the Complex Method, which can be used in solving a broad spectrum of problems. The method is a multivariable, direct-search technique that is efficient and convenient in optimizing problems with nonlinear objective functions subject to inequality constraints on explicit or implicit variables. This method has been applied successfully to many problems in the chemical industry; however, the applicability of this method for solving oilfield problems apparently has not been recognized. In this paper, two oilfield problems, a push-pull steam stimulation process problems, a push-pull steam stimulation process and a well-drilling schedule, were optimized using the Complex Method. The results were compared with those obtained by other optimization techniques reported in the literature. For both problems, the Complex Method was as efficient as other methods and probably was more efficient in obtaining the global optimum, both in terms of the number of objective-function evaluations required and of computing time. The solution to the constrained push-pull steam stimulation process was obtained push-pull steam stimulation process was obtained in one-fourth the number of evaluations required with the Hooke and Jeeves search technique; the solution to the drilling problem with 48 variables was obtained in only 2,123 objective-function evaluations, or 29 seconds of computing time on an IBM 370/165. Through the solution of two problems, the Complex Method was demonstrated to be easily applied and effective in obtaining optimum solutions as compared with other methods. This method should be implemented easily in obtaining optimum solutions as compared with other methods. This method should be implemented easily in obtaining optimum solutions to other oilfield problems. Introduction In recent years, the application of optimization techniques to oilfield problems has become widespread because of the possibility of increased profits or reduced costs with implementation of such studies. Several types of oilfield problems have been optimized using a wide variety of optimization techniques. E. L. Dougherty conducted an extensive review of the major applications of optimization techniques to oilfield problems. in these studies, the authors used a variety problems. in these studies, the authors used a variety of optimization techniques because of the difficulty of selecting an effective method for a particular problem. The Complex Method is a general optimization technique that can be applied directly to a variety of nonlinear problems with inequality constraints. The method is a problems with inequality constraints. The method is a multivariable direct-search technique; thus, the application of this method is especially convenient when derivatives of the objective function are difficult to obtain. The broad applicability of the Complex Method has been demonstrated in the chemical industry by successfully optimizing problems ranging from absorber-strippers to nonisothermal polymerization reactors. The method is implemented easily and is efficient in obtaining the global optimum while imposing inequality constraints on explicit and implicit variables. The objective of this paper is to demonstrate the usefulness and effectiveness of the Complex Method in obtaining the optimum values for oilfield problems, as compared with other methods. Two oilfield problems that previously have been solved by other methods were optimized using the Complex Method. The sample problems were the following:the optimum cycle length and the amount of steam injected in successive cycles are determined for a push-pull steam stimulation process such that the cumulative discounted net income is maximized; andthe optimum set of rotary speeds and weights on a bit is determined such that the drilling cost per foot is minimized in a drilling operation. These problems were selected to illustrate the wide range of mathematical formulations for which the Complex Method is applicable. The variable weight-speed schedule was selected for optimization rather than the constant weight-speed schedule because of the complexity of the variable weight-speed problem. SPEJ p. 123

The two-point boundary value problem with a small parameter in the theory of a reactor with a nonhomogeneous fluidized bed: PMM vol. 40, n≗ 4, 1976, pp. 641–647

A method based on the asymptotic joining of expansions is developed for solving the two-point boundary value problem for a system of equations with a single small parameter (high Péclet number) that occur in the theory of isothermal reactors with nonhomogeneous fluidized bed. External analytic solution in the form of a series containing three terms is derived for the case of small coefficient of exchange between bubbles and medium. An analytic solution of the problem is presented. It is uniformly valid over the whole segment and accurate to within quadratic terms containing the small parameter, which appear in the two-point boundary value problem. Models of reactors with a nonhomogeneous fluidized bed (see, e. g. [1–4]) are based on the concept of the fluidized bed as a two-phase system consisting of a continuous phase moving in the reactor at the initial fluidization rate, and of a discrete phase which is the excess of the fluidizing agent which moves through the bed in the form of bubbles. The computation of such type of reactor in the case of a reaction of an arbitrary order is complicated even in the one-dimensional case and can only be carried out by numerical methods. Because of this, approximate methods of nonlinear mechanics are of particular interest, for instance, for the computation of the steady mode of reactor operation. A method of solving the steady state equation for the isothermal reactor at high Péclet numbers was developed, based on the joining of asymptotic expansions. Later, a method similar to that of joining asymptotic expansions was proposed in [7] for solving equation of the isothermal reactor. However the extension of that method to systems of equations presents some difficulties [8–10]. Due to the nonlineari ty of equations of the nonisothermal reactor it was not possible to obtain an external analytic solution in the zero and subsequent approximations.

A radial cell model for a tubular polymerization reactor

AbstractA cell model for the prediction of temperature and concentration gradients in a nonisothermal tubular polymerization reactor at steady state is presented. Both radial and longitudinal gradients are considered. The complete molecular weight distribution is calculated as well as the leading moments of the distribution. The model is easily reduced to predict the performance of a plug‐flow tubular reactor, batch reactor, and continuous stirred tank reactor (CSTR). The specific polymerization mechanism application consists of free‐radical initiation, propagation, and combination termination.

Forced Oscillations in a Nonisothermal Continuous Polymerization Reactor

Abstract A dynamic model of a nonisothermal continuous stirred tank polymerization reactor is developed to predict product molecular weight distribution parameters. Deliberate oscillations in operating variables were programmed into the model and the resulting time-averaged reactor performance indices compared with that for optimum steady-state operation. Results indicate that periodic operation does influence polymerization reactor performance, particularly with regard to time-averaged molecular weight polydispersity. Significant resonant behavior was encountered with molecular weight properties at low frequencies.

Dynamics of open chemical systems and the algebraic structure of the underlying reaction network

While there has been a longstanding interest in stability of non-isothermal reactors there has only recently developed a comparable interest in the dynamics of open isothermal reactors with complex chemical reaction networks. In the recent literature there has been paid particular attention to the study of biological reaction systems which might exhibit sustained oscillations (biological clocks) or bistability (biological switches). Results are presented which bear upon the relationship between the algebraic structure of the underlying reaction network and the extent to which reactors might give rise to such “exotic” dynamics.

The backflow cell model—applied to non-isothermal reactors

Steady and unsteady state temperature profiles were measured in a non-isothermal liquid phase tubular reactor employing a highly exothermic reaction. For the evaluation of the results it was necessary to determine the dispersion coefficients at steady state conditions of the reactor since density differences caused by the temperature increase considerably decreased the dispersion. The backflow cell model was applied to explain the measured temperature profiles and a satisfactory agreement between measured and computed results was obtained. The backflow cell model is of advantage because the mathematical treatment is simple as shown by a numerical investigation for multiple states in axial-dispersed reactors.

Nonisothermal Chemical Kinetics

IN a recent article1, MacCallum and Tanner suggest that the traditional homogeneous reaction rate expression is applicable only to isothermal processes, and that an additional term should be added when the temperature varies over the course of the reaction. This suggestion has several disturbing features. It implies, contrary to logic, that the instantaneous reaction rate depends not only on the present state of the system (the frequency of collisions and relative energies and orientations of all of the system molecules) but also—through dT/dt—on previous and future states. The proposed correction is impossible to calculate, because in a real system temperature cannot be varied holding time constant, and therefore the factor (∂C/∂T)t is devoid of physical meaning; moreover, even for the hypothetical case of a step-function change in temperature, the instantaneous change in concentration must be 0, which eliminates the correction. A particularly far-reaching implication of the suggestion is that essentially all of the nonisothermal reactor modelling and analysis that has taken place over the past 80 years has been fundamentally unsound, by virtue of having been based on equation (1).

Heat transfer and kinetics in a catalyst bed of rectangular cross section: Air oxidation of nitric oxide with silica gel

AbstractThe results of an investigation of heat transfer and reaction kinetics in a fixed‐bed catalytic reactor of slab geometry are described. The particular reaction studied is the air oxidation of nitric oxide with silica gel. Conversions and catalyst‐bed temperatures were observed in the experimental, nonisothermal slab reactor, but only a sample of these data are reported and analyzed here.A mathematical analysis of the processes occurring in a slab reactor has been developed which leads to a design method for such reactors that permits prediction of catalyst‐bed temperatures and conversions from a knowledge of specific reaction rates and the physical properties of the system. The design method involves a step‐by‐step procedure but requires a small number of steps. To evaluate the accuracy of the design method and to illustrate its use, the specific reaction‐rate data together with published thermal‐conductivity data have been used with the method to predict the results of a run on the experimental nonisothermal reactor. Good agreement between calculated and observed temperatures and conversions was obtained.Specific reaction rates, derived from integral conversions in an experimental, isothermal reactor, are reported.